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Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and exhaustive simulations. Very often such codes incorporate heuristics that ironically make them less tractable and transparent. This paper introduces an active learning methodology for adaptively constructing surrogate models, i.e. emulators, of such costly computer codes in a multi-output setting. The proposed technique is sequential and adaptive, and is based on the optimization of a suitable acquisition function. It aims to achieve accurate approximations, model tractability, as well as compact and expressive simulated datasets. In order to achieve this, the proposed Active Multi-Output Gaussian Process Emulator (AMOGAPE) combines the predictive capacity of Gaussian Processes (GPs) with the design of an acquisition function that favors sampling in low density and fluctuating regions of the approximation functions. Comparing different acquisition functions, we illustrate the promising performance of the method for the construction of emulators with toy examples, as well as for a widely used remote sensing transfer code.
Earth observation from satellite sensory data poses challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression has excelled in biophysical parameter estimation tasks from airborne and sat
We present a novel Graphical Multi-fidelity Gaussian Process (GMGP) model that uses a directed acyclic graph to model dependencies between multi-fidelity simulation codes. The proposed model is an extension of the Kennedy-OHagan model for problems wh
Refining low-resolution (LR) spatial fields with high-resolution (HR) information is challenging as the diversity of spatial datasets often prevents direct matching of observations. Yet, when LR samples are modeled as aggregate conditional means of H
Many methods have been proposed to quantify the predictive uncertainty associated with the outputs of deep neural networks. Among them, ensemble methods often lead to state-of-the-art results, though they require modifications to the training procedu
We consider the problem of optimizing a vector-valued objective function $boldsymbol{f}$ sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space $({cal X},d)$ of designs. We assume that $boldsymbol{f}$ is not know